Question

Question 1 Futurists and science-fiction authors have often imagined circu ity",inwhich humans (or other thingsaccustomed to gravity) occupy a ring-shaped habitat. The ring rotates around a central hub, creating the impres- sion of gravityforitsinhabitants. They feel heavy, objects that they drop fall to the floor, and they otherwise experience all of the same things that people on a planet do lar spacecraft with "artificial grav- Inner pan uter panel Imagine that such a ship has a radius of R and is in deep space, where there is almost no (actual) gravity. Suppose that the crew of the ship wants the passengers to experience "artificial gravity" similar to that on Earth. (In an actual station R would be much larger than the height of people; this drawing is not to scale.) a) b) Explain how this works. Why does a rotating, ring-shaped spacecraft simulate gravity for its inhabitants? Specifically, what force presses them against the floor? If there is no such force, then explain why a person on such a spacecraft standing on a scale could see the same reading as they would on Earth, and why an object that they drop falls to the floor. (8 points) c) At what rate must the spacecraft rotate so that the people aboard experience artificial gravity that feels equal to Earth's? Give your answer in terms of g and R This station is powered by solar panels of mass m connected by cables to the central hub. A cable of length runs from the hub to the inner panel, a second cable runs from the inner panel to the outer panel. These solar panels also rotate along with the rest of the station at the same angular velocity d) Draw a force diagram for the inner solar panel and the outer solar panel. (Note that the tension in the two cables is different.) (5 points) e) In terms of m. R. and ω, calculate the tension T1 in the cable between the hub and the inner solar panel, and the tension T2 in the cable between the inner solar panel and the outer solar panel. (7 points)

Answer 1

Given the ship has a radius 'R' and a deep space Given there is almost no gravity The inhabits of the space ship feels the artificial gravity because of the centripetal force due to the rotational motion of the ship. When the body is rotated, it is always subjected to the center of rotation, known as the centripetal force which is given by the formula F_c = M w^2 R The centripetal acceleration Should be equal to gravitational acceleration. And the centripetal force should be equal to gravitational force. So, F_c = mg = m w^2 R w^2 = g/R therefore w = squareroot g/R \r\n force diagram for inner solar panel and the outer solar panel is The tension on the inner panel and heads will be the centripetal force on the inner panel T_1 = n mw^2 (R/2) T_1 = m g/R (R/2) therefore T_1 = mg/2 The force between outer panel and inner panel will be the centrifugal force on the outer panel.